Suppose our starship comes across a Class M planet, with no signs of civilization but surrounded by a very sophisticated defense array, totally automated. It simply doesn't react as the Enterprise (or whatever) nears. But sensors show the planet's ecosystem is breaking down very quickly, due to millions and millions of eggs hatching on the planet's surface. The creatures hatching are devouring everything in site, as well as fighting each other for scarce resources. An away team sent down gets into danger, while the array activates instantly when the Enterprise tries to stun an area so as to examine the newly-hatched creatures. The array drives the ship off, stranding the away team.

So the Reliant goes to rescue the crewman, now threatened as the creatures wake up. Landing, they have to de-cloak to pick up the survivors. The array tracks their position and damages the ship as it flees in cloak.

Later, members of the Away Team report on their findings. The creatures in the equivalent of a shark's feeding frenzy show signs of sentience, but are clearly very immature. The planet itself is terraformed.

In a later episode, they come across a damaged ship of strange design. Only a few survivors, clearly adults of the ravaging species on the planet. The whole ship gets superparanoid, especially since a distress call is attracting another such ship, what looks like a dreadnought. The survivors, badly wounded, die. So Enterprise hides from the dreadnought, giving their scientists time to analyze these aliens--who seem made for battle.

Still later, Enterprise makes contact with a civilization barely space-capable but who have legends of such creature--Sky Demons who eat children.

But when Enterprise encounters these Sky Demons for themselves, they find a very civilized race who seem to worship the idea of evolution. They terraform planets to allow their young to fight for survival, and afterwards "fix" the planets' ecosystems, to use it again in a century or so. But these aliens consider themselves in competition with themselves and with the universe, no one else. And hold up a mysterious people called "The Patrons" as the ideal towards which they strive. Indeed, contact with The Patrons led them to forgo rampant militarism in favor of self-improvement.

So--a member race of the League that seem incredibly dangerous, but civilized, but just maybe fanatics. And what if these Patrons told them to conquer the Federation?

That's an example of what I mean in terms of how contact with the League might play out.